8. In the figure, AB ll CD, <ABE = 130˚ and <CDE = 170˚. Find <BED.
Answers
Step-by-step explanation:
Here we extend line AB as that meet line DE at " X " , so AX | | CD ( as given AB | | CD and AB is part of AX )
∠ CDE = ∠ AXE = 80° --- ( 1 ) ( Corresponding Angles , AX | | CD and DE is transversal line and ∠ CDE = 80° is given )
Now from angle sum property of triangle we get in triangle BEX :
∠ BEX + ∠ AXE + ∠ XBE = 180° , Substitute values , As ∠ BED = ∠ BEX = 40° , same angles and from equation 1 we get
40° + 80° + ∠ XBE = 180°
∠ XBE = 60° --- ( 2 )
And
∠ XBE + ∠ ABE = 180° ( Linear pair angles )
60° + ∠ ABE = 180° ( From equation 2 )
∠ ABE = 120° ( Ans )
Answer:
Step-by-step explanation:
Extend line AB as that meet line DE at " X " , so AX | | CD ( as given AB | | CD
and AB is part of AX )
∠ CDE = ∠ AXE = 80° --- ( 1 ) ( Corresponding Angles , AX | | CD and DE is
transversal line and ∠ CDE = 80° is given )
Now from angle sum property of triangle we get in triangle BEX :
∠ BEX + ∠ AXE + ∠ XBE = 180° , Substitute values , As ∠ BED = ∠ BEX = 40° ,
same angles and from equation 1 we get
40° + 80° + ∠ XBE = 180°
∠ XBE = 60° --- ( 2 )
∠ XBE + ∠ ABE = 180° ( Linear pair angles )
60° + ∠ ABE = 180° ( From equation 2 )
∠ ABE = 120°